The present invention is directed to a method for predicting stability characteristics of single and multiple paralleled power supplies under arbitrary load conditions. The present invention is particularly directed to a method for predicting stability characteristics for direct current, DC-to-DC, power supplies.
Thottuvelil and Verghese characterized a power converter as a Thevenin voltage source model in their paper setting forth a small-signal stability analysis of paralleled DC-DC converter systems. (See, V. Joseph Thottuvelil and George C. Verghese; xe2x80x9cAnalysis and Control Design of Paralleled DC/DC Converters with Current Sharingxe2x80x9d; IEEE Transactions on Power Electronics, Vol. 13, No. 4; July 1998.) The inventor of the present invention has employed a similar model, but for a different purpose: to analyze DC-DC power converter apparatus for improving predictions regarding stability of individual power converter apparatuses.
When designing power supply, or power converter circuits, one must take into account the potential user""s load characteristics. This consideration is especially important in the design of DC-DC converters because such converters are generally configured as a closed loop system that monitors its output, provides feedback indicating its output, and employs the feedback to adjust to maintain a constant DC output. In any feedback system, it is of significant importance that the feedback loop be stable. A simple example of an unstable feedback loop is the loud tone produced in the presence of audio feedback when a microphone is placed too close to a speaker producing signals originating at the microphone.
Today""s electronic devices are more and more designed to be , smaller, and more reliable. This trend for product requirements is especially evident in portable electronic devices such as cellular telephones, electronic games, and portable computers. Some practical design consequences of this trend are that output voltages for DC-DC converters are getting lower and the stability of output of DC-DC converters is more critical. Nyquist developed criteria to assess the stability of a control loop (xe2x80x9cRegeneration Theoryxe2x80x9d, H. Nyquist, Bell System Technical Journal, January 1932). Bode (xe2x80x9cRelations Between Attenuation and Phase in Feedback Amplifier Designxe2x80x9d, Bell System Technical Journal, July 1940) expressed these criteria in terms of the phase (xcfx86) and gain of a transfer function According to this analysis, if gain (dB) and phase change (xcex94xcfx86) of the loop gain are zero at the same frequency in a circuit, the circuit will be unstable.
As a practical engineering measure, one must design a circuit having xe2x89xa745xc2x0 phase margin to reliably have a stable circuit. Phase margin is the value of phase when gain as a function of frequency crosses through zero from positive to negative. Thus, when gain is 0 dB, and gain is passing from positive to negative, phase must be xe2x89xa745xc2x0 in order for the circuit under consideration to be stable with adequate margin.
Another measure of stability is to require that gain margin be xe2x89xa7xe2x88x927 to xe2x88x9210 dB. That is, when phase as a function of frequency crosses through zero, gain must be at least 7-10 dB in order that the circuit under consideration will be a stable circuit
The fact that a user""s load characteristics figure so intimately in stability of DC-DC converter circuits, and the ever more stringent requirements for greater stability at lower voltages for modem electronic circuits have made present ways of predicting stability of a particular DC-DC converter circuit for a particular application uneconomical and not particularly reliable or accurate.
Presently, manufactures of power supplies, and especially of DC-DC converters, use simulations, or laboratory measurements, or closed form analytical expressions, or all tree of those methods for determining whether a particular circuit is stable with a particular load. Simulations are expensive in that they occupy large amounts of computer capacity and time. Closed form analytical expressions rely on simplifying assumptions that introduce significant errors. Laboratory measurements are an expensive approach to answering questions about a particular circuit-load stability in terms of human time and computer assets involved. Further, neither simulations, closed form analytical expressions nor laboratory experimentation are particularly accurate in predicting ability of converter apparatuses under various load conditions.
One result of ongoing efforts to predict stability with arbitrary loads is that man of power converters must essentially custom-tailor their products to user""s loads on a case-by-case basis. Such a xe2x80x9cjob shopxe2x80x9d approach to production precludes one""s taking advantage of the economies of scale which could be enjoyed if a manufacturer could predict which loads were amenable to stable use with particular converters. That is, if manufacturers could predict stability for a particular converter circuit within established limits for a definable range of load characteristics, then families of converter products could be manufactured and the inefficiencies of customizing converter circuits for each discrete load criterion may be avoided
There is a need for a method for predicting stability characteristics of power converters under arbitrary load conditions. This need is particularly acute in predicting stability characteristics of DC-DC power converter circuits.
The preferred embodiment of the present invention is a method for determining the effect of load impedance on the magnitude and phase of loop gain of a power converter apparatus to aid in predicting stability of the converter apparatus under various operating conditions. The converter apparatus has an open-loop output impedance and provides an output signal to an output locus. The method comprises the steps of: (a) vectorally measuring a first loop gain of the converter apparatus with a first load impedance connected with the output locus, to record phase and gain of the first loop gain for a plurality of frequencies; (b) vectorally measuring open loop output impedance as a function of frequency of the converter apparatus, to record phase and gain of the open loop output impedance for a plurality of frequencies; (c) vectorally measuring the first load impedance as a function of frequency of the converter apparatus, to record phase and gain of the first load impedance for a plurality of frequencies; (d) calculating a first load distribution factor using the first load impedance and the open-loop output impedance; the calculating being effected in vectoral manner to record magnitude and phase of the first load distribution factor for a plurality of frequencies; (e) selecting a second impedance load with an output voltage sense point, the second impedance load being representable by a network of at least one resistor and at least one capacitor or inductor, the output voltage sense point being situated at a selected node of the network; (f) calculating a second load distribution factor for the second impedance load using the open-loop output impedance and the second impedance load; the calculating being effected in vectoral manner to record magnitude and phase of the impedance-loop load distribution factor for a plurality of frequency values; and (g) calculating a second loop gain using the first loop gain, the fist loop load distribution factor and the second loop load distribution factor; the calculating being effected in vectoral manner to record magnitude and phase of the impedance-load gain for a plurality of frequency values.
One example of the application of the method of the present invention is generation of a Stable Operating Area Plot. By employing the method of the present invention one can plot contours of constant phase margin as a function of the resistive and reactive portions of the arbitrary second load network. Such a plot facilitates identifying stable operating ranges for selected load impedances. Information regarding stable operating parameters provides a product designer with a valuable tool for assessing stability of a particular converter apparatus under a variety of loading conditions. The reference tool may be in the form of a multidimensional graphic relation of gain, phase and frequency data. Alternate ways to create such a reference tool include a multidimensional vectoral table. Such a vectoral table may be maintained on-line for access by software inquiry, or it may be produced in printed or other form.
It is, therefore, an object of the present invention to provide a method for determining relationships among magnitude and phase of loop gain, open loop output impedance and load impedance for a power converter apparatus to aid in predicting stability of said converter apparats under various operating conditions.